The paper studies bifurcations in delay differential equations (DDEs) with distributed delays. The local stability analysis is performed, using the Routh-Hurwitz citerion, only for the two cases of exponential integral kernels
(called the weak kernel in the article) and
(called the strong kernel). Both of these special cases allow one to reduce the DDE to an ordinary differential equation (ODE). The analysis of the criticality of the Hopf bifurcation is performed for general kernels and then discussed more specifically for the two exponential kernels.